An investigation of matched index of refraction technique and its application in optical measurements of fluid flow

Optical distortions caused by non-uniformities of the refractive index within the measurement volume is a major impediment for all laser diagnostic imaging techniques applied in experimental fluid dynamic studies. Matching the refractive indices of the working fluid and the test section walls and interfaces provides an effective solution to this problem. The experimental set-ups designed to be used along with laser imaging techniques are typically constructed of transparent solid materials. In this investigation, different types of aqueous salt solutions and various organic fluids are studied for refractive index matching with acrylic and fused quartz, which are commonly used in construction of the test sections. One aqueous CaCl₂·2H₂O solution (63 % by weight) and two organic fluids, Dibutyl Phthalate and P-Cymene, are suggested for refractive index matching with fused quartz and acrylic, respectively. Moreover, the temperature dependence of the refractive indices of these fluids is investigated, and the Thermooptic Constant is calculated for each fluid. Finally, the fluid viscosity for different shear rates is measured as a function of temperature and is applied to characterize the physical behavior of the proposed fluids.     

The effect of astigmatism due to beam refractions on the formation of the measurement volume in LDA measurements

The accuracy of LDA measurements depends on the optical alignment of the laser beams. Improperly designed optical systems lead to fringe distortion in the measurement volume and in earlier investigations this effect has always been taken as the main cause of optical inaccuracy in LDA measurements. In the present work a different cause of fringe distortion is considered: astigmatism due to beam refractions. A quantitative theory for the astigmatism of laser beams is derived for both single and multiple refractions. Parameter calculations with regard to the size of the astigmatism effect have been carried out. It is shown that astigmatism is a relevant parameter which influences the fringe uniformity and fringe distortion in an LDA measurement volume and affects the measurement accuracy of measurements in internal flow. The equations derived enable the change in cross sections of the refracted laser beams to be determined. The spatial deviations of the diverse focusing points of refracted laser beams relative to the position of the LDA measurement volume are found to depend strongly on the incident angle of the beams and therefore on the off-axis alignment angle of the LDA probe (off-axis from the normal to the flow-wall-interface).     

Application of particle image velocimetry to combusting flows: design considerations and uncertainty assessment

Methodological aspects concerning the application of the PIV technique to the study of turbulent flames are discussed in this paper. The physical features of the flow, which have implications for the experimental set-up, image processing and measurement accuracy are identified. Design considerations are developed focusing on several factors: spatial resolution, particle performance, seeding technique, image formation and recording, and image post-processing for the evaluation of the displacement. Relevant uncertainty concerns are related to the effect of the thermophoretic force, acting on a seeding particle while crossing the flame front, and to the non-homogeneity and time-dependence of the refractive index field. The uncertainty due to thermophoresis is assessed by numerically studying the motion of a particle crossing a reference temperature profile. The effect of the refractive index variation is evaluated by means of theoretical analysis of light propagation and image formation, supported by experimental tests designed for this special purpose. Received: 25 November 1999/Accepted: 31 March 2000     

Optical guidelines and signal quality for LDA applications in circular pipes

The optical performance of laser Doppler anemometer (LDA) technology in applications to circular pipes with an external plane wall has been clarified and quantified. It is shown that optical aberration is a persistent feature in such LDA measurements and measurements from each direction along a full pipe diameter are needed to obtain the flow distribution. For measurements of axial velocities in a circular pipe no special care has to be taken, even if the optical plane deviates from the pipe axis. For measurements of tangential and radial velocities detailed operating guidelines have been presented with respect to the shift of the measurement volume, its optical properties and the beam waist dislocations. The analysis reveals the possible influences on both the signal quality and the measurement accuracy.     

A large-scale matched index of refraction flow facility for LDA studies around complex geometries

Useage of laser-Doppler anemometry (LDA) requires optical access to the flow field of interest. This has not always proved easy, as in the case of complex geometries or very near-wall boundary layer measurements. One solution is to employ a solid material and fluid with the same refractive index. In this case, there is no optical interference of the solid with the LDA. Although this technique is not new, previous studies have been limited to small flow apparatus and relatively unpleasant fluids. A large-scale flow tunnel has now been constructed, permitting matched index of refraction LDA measurements in difficult geometries, higher Reynolds numbers, and increased spatial resolution in the measurements. This paper describes the facility and fluid flow quality, and presents some preliminary results for very near-wall measurements of a transitional boundary layer behind a roughness element. Received: 13 March 2000/Accepted: 30 July 2000     

GRIN介质用于面内位移的测量

本文把梯度折射率（ＧＲＬＮ）介质的面内位移与其折射率梯度联系起来,对面内位移导致的折射率变化进行研究,介绍了ＧＲＩＮ介质用于面内位移测量的基本原理,给出了双光束干涉法测量悬臂梁挠度的实验方法和实验结果     

A synthetic Schlieren method for the measurement of the topography of a liquid interface

An optical method for the measurement of the instantaneous topography of the interface between two transparent fluids, named free-surface synthetic Schlieren (FS-SS), is characterised. This method is based on the analysis of the refracted image of a random dot pattern visualized through the interface. The apparent displacement field between the refracted image and a reference image obtained when the surface is flat is determined using a digital image correlation (DIC) algorithm. A numerical integration of this displacement field, based on a least square inversion of the gradient operator, is used for the reconstruction of the instantaneous surface height, allowing for an excellent spatial resolution with a low computational cost. The main limitation of the method, namely the ray crossing (caustics) due to strong curvature and/or large surface-pattern distance, is discussed. Validation experiments using a transparent solid model with a wavy surface or plane waves at a water–air interface are presented, and some additional time-resolved measurements of circular waves generated by a water drop impact are discussed.     

Precise flow rate measurements of natural gas under high pressure with a laser Doppler velocity profile sensor

This paper reports about the first application of a laser Doppler velocity profile sensor for precise flow rate measurements of natural gas under high pressure. The profile sensor overcomes the limitations of conventional laser Doppler anemometry (LDA) namely the effect of spatial averaging and the effect of fringe spacing variation (virtual turbulence). It uses two superposed, fan-like interference fringe systems to determine the axial position of a tracer particle inside the LDA’s measurement volume. Consequently, a spatial resolution of about 1 μm can be achieved and the effect of virtual turbulence is nearly eliminated. These features predestine the profile sensor for flow rate measurements with high precision. Velocity profile measurements were performed at the German national standard for natural gas, one of the world′s leading test facilities for precision flow rate measurements. As a result, the velocity profile of the nozzle flow could be resolved more precisely than with a conventional LDA. Moreover, the measured turbulence intensity of the core flow was of 0.14% mean value and 0.07% minimum value, which is significantly lower than reference measurements with a conventional LDA. The paper describes the performed measurements, gives a discussion and shows possibilities for improvements. As the main result, the goal of 0.1% flow rate uncertainty seems possible by an application of the profile sensor.     

Measurement of 3D pore-scale flow in index-matched porous media

We present the experimental analysis of fluid flow at the pore-scale of a transparent porous medium with matched refractive indices of the solid and liquid phases. The planar laser-induced fluorescence (PLIF) technique described is the first to simultaneously visualize the 3D pore-scale flow of two immiscible liquid phases in porous media. Through the application of a highly precise index matching method and the employment of up-to-date CCD imaging hardware, the system features a high spatial resolution and sampling rate. The method was used to study the dispersion of a tracer dye in single-phase flow and the displacement of oil by water in an imbibition process.     

基于连续正弦速度扫描方式的激光多普勒测振技术

本文针对逐点扫描激光多普勒非接触测振技术只能进行离散空间域振动测试的缺陷,研究了基于连续正弦速度扫描方式的激光多普勒测振新技术,实现了连续空间域的振动测试。并以简支梁为测试对象,进行了实验验证。实验结果表明:应用连续扫描激光多普勒测振技术与扫描激光多普勒测振技术获取的模态振型匹配一致,而且前者在测试时间、测试数据量及空间分辨率上都优于后者。     

Experimental investigation on the influence of gap vortex streets on fluid-structure interactions in hexagonal bundle geometries

Gap vortex streets characterise many industrial applications involving rod bundle flows, such as heat exchangers and nuclear reactors. These structures, known as gap vortex streets, may excite the structural components of the bundle to resonance, leading to fretting and fatigue. This work aims to measure these coherent structures and the resulting displacement and oscillation frequency of the neighbouring rod, to provide unique data for fluid-structure interaction studies and to develop a general correlation for estimating the coherent structure’s wavelength. A water loop was built to host a hexagonal rod bundle. Fluorinated Ethylene Prophylene (FEP), a refractive index matching (RIM) material, was used to have undisturbed optical access in the area around the central rod. The flow was measured with Laser Doppler Anemometry (LDA) to detect coherent structures, while the vibrations were measured with a high speed camera. A new correlation for estimating the wavelength of the coherent structures is derived with dimensional analysis based on experimental evidence. The correlation is tested on different geometries: rectangular channels with single or half-rods, and two rod bundles, within the pitch-to-diameter ratio (P/D) range 1.02–1.2. Moreover fluctuations in the flow, given by the detected coherent structures, govern the structural response of the rod. The rod is excited to resonance if these fluctuations match twice the natural frequency of the rod.     

Distortion of LDA fringe pattern by tracer particles

For precise flow velocity measurements laser Doppler anemometry (LDA) is wide-spread in use in the laboratories of industry and universitarian research institutions. The LDA method has the advantage of being not intrusive and able to discriminate between forward and reverse velocities. So far, laser Doppler anemometry is believed to be one of the most accurate flow measuring techniques. However, recent investigations have shown that the period lengths of LDA signal bursts are not constant within an individual burst. This can induce an additional scatter in the signal frequency and in the determination of the flow velocity. Until now, the reason for the period variations has not been investigated in detail although the problem was observed before. This paper describes experimental investigations which show that the particle passage through the laser beams shortly before the point of superposition, i.e. the LDA measuring volume, yields a distorted LDA fringe pattern. Thus, the signal period length from an individual particle, passing the center of the measuring volume at the same time, varies according to the distortion of the fringe spacing.     

Slip velocity measurements in an upward bubbly flow by combined LDA and electrodiffusional techniques

 An experimental technique for the measurement of the local slip velocity of spherical bubbles is reported. It is based on the measurement of the local liquid velocity by an electrodiffusional method, and the bubble velocity by a specially adapted LDA (Laser Doppler anemometer) with a short measuring volume. The bubble velocity is measured taking into account the shift between the bubble centre and the centre of the LDA measuring volume. The slip velocity is obtained by subtracting the liquid velocity from the bubble velocity at the point corresponding to the bubble centre. The technique is applicable for flows with high velocity gradients. Results of the slip velocity measurements in an upward bubbly flow at laminar pipe Reynolds numbers are presented. Received: 25 July 1996/Accepted: 13 April 1998     

Determination of the measuring position in laser-Doppler anemometry

The present paper is concerned with the determination of the measuring position of a laser-Doppler anemometer (LDA) relative to a wall. The proposed method is based on the finding that the output of a hot-wire anemometer increases when the wire, which is mounted in quiescent air parallel to the wall, is brought closer than 800 m to the wall. For given hot-wire anemometer parameters, the hot-wire anemometer output voltage depends on the wall material and the wire distance from the wall. After suitable calibration for the wall material of the test section, the anemometer reading in a test rig can be used to find the wire position. Moving the measuring volume of a LDA-system across the wire yields an output voltage variation of the LDA-photomultiplier showing a Gaussian shape. When the maximum output voltage is reached, the centre of the measuring control volume is located at the centre of the wire and, hence, the location of the LDA-measuring position is known. All position measurements for the LDA-system are then taken relative to this point using the scale of the LDA-traversing system. If optical effects of transparent test section walls are eliminated by employing refractive index matched liquids, there are other ways to find the measuring position of a laser-Doppler anemometer relative to a wall. One such method and its application to the study of the turbulent near wall flow in a pipe is described in this paper.     

Effect of particle polydispersity on particle concentration measurement by using laser Doppler anemometry

Measurement of particle concentration by laser Doppler anemometry (LDA) is studied on a vertical air jet seeded by a powder disperser with controlled particle and air flow rates. Particle arrival rate is utilized to retrieve particle number densities from conventional LDA operation. The effect of polydisperse nature of the particles is assessed. Comparisons between measured and estimated particle number densities suggest that only a certain portion of the particle population with a particle size to fringe spacing ratio around unity can be detected. Results indicate that reliable measurement of absolute particle concentration is possible for a particle population of narrow size distribution with an average diameter equivalent to fringe spacing. Present number density measurement technique which is useful for practical purposes with conventional LDA systems is found to yield physically reasonable profiles in both laminar and turbulent regimes.     

离心力对干涉测量光路的影响及其修正

本文分析了旋转载体上离心力造成的干涉测量光路中空气介质压强的不均匀变化，给出了与光路介质折射率相应的分布规律，分析了由此引起的干涉测量系统动态测量的示值偏差，据此分析计算的结果可用于测量结果的精密修正。本文的讨论结果为精密离心机及类似的运动载体上的动态干涉测量系统的分析设计提供了依据。     

Irregular particle sizing using speckle pattern for continuous wave laser applications

We present velocity power spectra computed by the so-called direct method from burst-type laser Doppler anemometer (LDA) data, both measured in a turbulent round jet and generated in a computer. Using today’s powerful computers, we have been able to study more properties of the computed spectra than was previously possible, and we noted some unexpected features of the spectra that we now attribute to the unavoidable influence of a finite measurement volume (MV). The most prominent effect, which initially triggered these studies, was the appearance of damped oscillations in the higher frequency range, starting around the cutoff frequency due to the finite size of the MV. Using computer-generated data mimicking the LDA data, these effects have previously been shown to appear due to the effect of dead time, i.e., the finite time during which the system is not able to acquire new measurements. These dead times can be traced back to the fact that the burst-mode LDA cannot measure more than one signal burst at a time. Since the dead time is approximately equal to the residence time for a particle traversing a measurement volume, we are dealing with widely varying dead times, which, however, are assumed to be measured for each data point. In addition, the detector and processor used in the current study introduce a certain amount of fixed processing and data transfer times, which further contribute to the distortion of the computed spectrum. However, we show an excellent agreement between a measured spectrum and our modeled LDA data, thereby confirming the validity of our model for the LDA burst processor.     

A high-resolution laser Doppler anemometer: design, qualification, and uncertainty

A new high-resolution laser Doppler anemometer (LDA) has been developed with a working distance of 350 mm, allowing operation in lab-scale wind tunnels. The measurement volume size is 35 μm in diameter by 60 μm in length, allowing resolution of the smallest turbulence scales even at fairly high Reynolds numbers. The controversial question of velocity and validation bias in LDA data is resolved with an experimental method for measuring and removing those effects. Uncertainty estimates are also derived for all the mean and Reynolds stress measurements. Received: 27 June 1999/Accepted: 30 August 2000     

Averaged temperature fields in asymmetrical turbulent streams over localized heat sources

A modification of the shadow method which can be used to measure the three-dimensional averaged fields of the refractive index in turbulent flows is described. The method is applied to the measurement of a temperature field in a turbulent convective flow. A stream of heated fluid flowing slowly out of a circular opening is used as the heat source. The measurement results are compared with asymptotic dependences for buoyant convective fluids [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 199–203, March–April, 1977.     

On the overestimation of the flow turbulence due to fringe distortion in LDA measurement volumes

 Fringe distortion with linear longitudinal variation in fringe spacing over the length of LDA measurement volume has been considered to influence the accuracy of flow measurement. The overestimation of the mean velocity and especially of the flow turbulence due to fringe distortion has been derived to be a function both of the fringe distortion number (which is a purely geometrical parameter of the measurement volume) and the flow turbulence to be measured. Against the usual expectation, it has been shown that the overestimation of the flow turbulence due to fringe distortion in the measurement volume could be neglected. Only for very low turbulence intensity dose the error become significant. As a reference this result could be used to estimate measurement errors which occur in the presence of other types of fringe distortion. Received: 2 December 1997/Accepted: 2 May 1998